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Unformatted text preview: A SHORT SUMMARY OF PROBABILITY THEORY NICHOLAS CRAWFORD Let us begin at the beginning. A model for probability theory consists of the following Definition 0.1 A Sample Space: A sample space, which we shall denote generically by S , consists of all possible outcomes from an experiment or collection of experiments. It is best to think of examples when trying to understand this terminology: Tossing a coin 3 times, S consists of all possible triples of Hs and Ts such as HHH, HTH, etc. Definition 0.2 An Event: An event on a sample space is an outcome or collection of outcomes in S . Most often an event is described in words rather than given as a list of allowed outcomes. For example the event A = { Second coin is heads and third is tails } is given instead of { HHT , THT } . In such a simple example it makes no difference how one respresents an event, but we have seen many examples where the descriptive definition is more efficient. Think, for example, about listing all possible outcomes which correspond to the event of winning the lottery exactly twice if we play 52 weeks in a row.the event of winning the lottery exactly twice if we play 52 weeks in a row....
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